Bayesian personalism, the methodology of scientific research programmes, and Duhem's problem

The detailed analysis of a particular quasi-historical numerical example is used to illustrate the way in which a Bayesian personalist approach to scientific inference resolves the Duhemian problem of which of a conjunction of hypotheses to reject when they jointly yield a prediction which is refuted. Numbers intended to be approximately historically accurate for my example show, in agreement with the views of Lakatos, that a refutation need have astonishingly little effect on a scientist's confidence in the ‘hard core’ of a successful research programme even when a comparable confirmation would greatly enhance that confidence . Timeo Danaos et dona ferentis
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Allan Franklin & Colin Howson (1984). Why Do Scientists Prefer to Vary Their Experiments? Studies in History and Philosophy of Science Part A 15 (1):51-62.
Hannes Leitgeb (2013). Reducing Belief Simpliciter to Degrees of Belief. Annals of Pure and Applied Logic 164 (12):1338-1389.

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